I have recently started learning about machine learning and have come across kernels and null spaces. I understand that null space is the set of all vectors that satisfy the equation A.v = 0 (Where A is a matrix). I have been taught that null space is a set of vectors that are squished to 0 when transformation matrix A is applied. Then I came across SVM where kernel functions are used. I read that null spaces are also called kernels of a matrix. My questions are as follows.
- Are both kernel functions and null spaces same? If they are related, how are they related?
- What is the relation between kernel functions used in SVM and null space of matrix? If yes, how? Is this derived from the null space of transformations used in SVM?
- What is the reasoning behind kernels used in kernel convolution? For example: Is the Gaussian kernel used a representation of the transformation? How are they related to null spaces? If they are related, how are they related?
I have already asked this in signal processing site and CV site. But, I haven't received any answer yet. Could you please answer these questions? I am very confused. Thank you in advance.